In our study, the idealized electron-positron-ion mixed target is assumed to be an overdense plasma with a pre-formed pair plasma. The charge neutrality is satisfied, i.e., \(n_e=n_p+Z_in_i\) , where \(n_e\) , \(n_p\)  and \(n_i\)  are the electron, positron and ion densities, respectively, and \(Z_i\)  is the ion charge state. For simplicity, this target is assumed to have immobile ions, a sharp interface (\(L_n\ll \lambda _0\) , where \(L_n=n/\nabla n\)  is the gradient length of plasma density and \(\lambda _0\)  is the laser wavelength) and uniform density distribution. The positron fraction is defined as \(\alpha =n_p/n_e\) . A \(p\) -polarized, weakly relativistic (\(a_0\lesssim 1\) ) laser is incident with angle \(\theta \) , where \(a_0\)  is the normalized field amplitude. The boost technique [1]}, [2]}, [3]} is employed here, enabling 1-dimensional (1D) studies on oblique laser incidence. Appendix  gives related notations and formalisms of this technique.
